Empirical Results

Overview: From Theory to Evidence

This chapter presents the main empirical findings from our INLA-BYM2 spatial analysis of correctional supervision patterns across Utah. The results demonstrate how environmental conditions, community characteristics, and spatial clustering patterns serve as conversion factors that shape capability formation and correctional outcomes.

ImportantKey Finding

Environmental justice emerges as the strongest predictor: A one standard deviation increase in diesel particulate matter is associated with a 494.7% increase in correctional supervision rates, even after controlling for poverty, demographics, and other socioeconomic factors.

1 Main Results: Conversion Factors and Capabilities

1.1 Fixed Effects: Direct Conversion Factor Impacts

1.1.1 Environmental Justice as Primary Conversion Factor

The most striking finding is the overwhelming impact of environmental conditions on correctional supervision outcomes:

• Diesel Particulate Matter: +494.7% increase (95% CI: 239% - 971%)
• Air Quality Index: Significant positive association
• Environmental burden: Compounds other disadvantages

1.1.2 Protective Conversion Factors

Several factors emerged as significant protective influences that enhance capability formation:

Community Engagement & Access

• Census Response Rate: -73.6% (Collective Efficacy)
• Automobile Access: -91.0% (Transportation)
• Bachelor’s Degree: -88.4% (Educational Access)

Economic & Health Security

• Health Insurance: -73.3% (Healthcare Access)
• Employment Rate: -50.0% (Economic Opportunity)
• Homeownership: -40.8% (Housing Stability)

2 Spatial Analysis: Collective Capabilities in Action

2.1 Relative Risk Mapping: Environmental Justice Patterns

The spatial analysis reveals stark geographic inequalities in capability formation:

NoteMap Interpretation

• Dark Red Areas: 2-3x higher correctional supervision rates than expected (severe capability constraints)
• Orange/Yellow Areas: Moderately elevated rates (1.2-1.8x expected)
• Light Areas: Lower than expected rates (strong collective capabilities)
• Spatial Clustering: Clear evidence that place-based factors matter significantly

2.1.1 Case Studies: Capability Extremes

High-Risk Example - Carbon County (RR = 2.42)

• 142% higher correctional population than expected
• Poor air quality (high diesel particulate matter)
• Limited transportation access
• Concentrated environmental hazards

Low-Risk Example - Morgan County (RR = 0.21)

• 79% lower correctional population than expected
• Better environmental conditions
• Higher collective efficacy
• Stronger community resources

3 Detailed Statistical Results

3.1 Model Performance and Spatial Components

Model Performance Statistics

Diagnostic	Value	Interpretation
DIC	5199.78	Lower is better - good model fit
WAIC	5073.35	Cross-validation based - strong predictive performance
Marginal Log-Likelihood	-2544.67	Higher is better - excellent model quality
Effective Parameters	355.10	Appropriate complexity for spatial model

Spatial Random Effects: Evidence for Collective Capabilities

Component	Value	Theoretical Interpretation
Spatial Structure (φ)	0.594	59.4% of spatial variation is structured (collective capabilities)
Spatial Precision (τ_u)	2.79	Strong spatial dependence between neighboring areas
Individual Variation (τ_v)	21,100	Low unstructured variation - spatial effects dominate

3.2 Complete Fixed Effects Results

# Reorder columns and sort data
results_df_reordered <- results_df %>%
  select(X, Variable, Coefficient, CI_Lower, CI_Upper, Elasticity, Significance, Category, everything()) %>%
  arrange(desc(Significance == "Significant"), desc(abs(Elasticity)))

# Create the datatable with reordered columns
DT::datatable(results_df_reordered,
              caption = "Complete INLA Model Results: Conversion Factors Analysis (Sorted by Significance)",
              options = list(
                columnDefs = list(list(className = 'dt-center', targets = 2:8)),
                pageLength = 15,
                scrollX = TRUE,
                dom = 'Bfrtip'
              ),
              rownames = FALSE) %>%
  formatRound(columns = c('Coefficient', 'CI_Lower', 'CI_Upper', 'Elasticity', 'CI_Lower_Elasticity', 'CI_Upper_Elasticity'), digits = 3) %>%
  formatStyle('Elasticity',
              backgroundColor = styleInterval(c(-0.5, 0.5), c("#d4edda", "#ffffff", "#f8d7da"))) %>%
  formatStyle('Significance',
              backgroundColor = styleEqual('Significant', '#e8f5e8'),
              fontWeight = styleEqual('Significant', 'bold'))

4 Interactive Network Diagram Environmental Connections

4.1 Interpretation

This interactive network shows how diesel particulate matter (highlighted in larger size) serves as a critical conversion factor that transforms environmental racism into criminal justice involvement through multiple pathways:

• Click on nodes to highlight connected pathways
• Hover for detailed explanations
• Drag nodes to rearrange the layout
• Use the legend to focus on specific categories

5 Policy Translation: From Evidence to Action

5.1 Priority Matrix for Intervention

policy_interventions <- data.frame(
  Rank = 1:8,
  `Policy Area` = c("Environmental Justice", "Transportation Access", "Educational Access", 
                    "Community Engagement", "Healthcare Access", "Housing Stability",
                    "Employment Programs", "Economic Development"),
  `Effect Size` = c("+494.7%", "-91.0%", "-88.4%", "-73.6%", "-73.3%", 
                    "-40.8%", "-50.0%", "Mixed"),
  `Evidence Level` = c("Very Strong", "Strong", "Strong", "Strong", "Strong",
                       "Moderate", "Moderate", "Moderate"),
  `Implementation Strategy` = c(
    "Environmental monitoring, pollution reduction, green infrastructure",
    "Public transit expansion, vehicle access programs, ride-sharing",
    "Community college access, adult education, workforce development",
    "Civic engagement initiatives, community organizing, participation programs",
    "Insurance enrollment assistance, community health centers, mobile clinics",
    "Housing rehabilitation, down payment assistance, tenant protections",
    "Job training programs, employment placement, skills development",
    "Small business development, entrepreneurship support, economic zones"
  )
)

kable(policy_interventions,
      caption = "Evidence-Based Policy Priority Matrix",
      col.names = c("Priority", "Policy Area", "Effect Size", "Evidence", "Implementation Strategy")) %>%
  kable_styling(bootstrap_options = c("striped", "hover"), font_size = 11) %>%
  column_spec(5, width = "35%") %>%
  row_spec(1, background = "#ffebee") %>%  # Highlight top priority
  row_spec(2:4, background = "#e8f5e8")    # Highlight strong protective effects

Evidence-Based Policy Priority Matrix

Priority	Policy Area	Effect Size	Evidence	Implementation Strategy
1	Environmental Justice	+494.7%	Very Strong	Environmental monitoring, pollution reduction, green infrastructure
2	Transportation Access	-91.0%	Strong	Public transit expansion, vehicle access programs, ride-sharing
3	Educational Access	-88.4%	Strong	Community college access, adult education, workforce development
4	Community Engagement	-73.6%	Strong	Civic engagement initiatives, community organizing, participation programs
5	Healthcare Access	-73.3%	Strong	Insurance enrollment assistance, community health centers, mobile clinics
6	Housing Stability	-40.8%	Moderate	Housing rehabilitation, down payment assistance, tenant protections
7	Employment Programs	-50.0%	Moderate	Job training programs, employment placement, skills development
8	Economic Development	Mixed	Moderate	Small business development, entrepreneurship support, economic zones

5.2 Protective Factors Visualization

protective_data <- data.frame(
  Factor = c("Census Response\n(Community Engagement)", 
             "Automobile Access\n(Transportation)", 
             "Bachelor's Degree\n(Educational Access)",
             "Health Insurance\n(Healthcare Access)",
             "Employment Rate\n(Economic Opportunity)",
             "Homeownership\n(Housing Stability)"),
  Risk_Reduction = c(73.6, 91.0, 88.4, 73.3, 50.0, 40.8),
  Theory_Connection = c("Collective Efficacy", "Mobility Access", "Human Capital", 
                       "Health Security", "Economic Stability", "Asset Building"),
  Category = c("Social", "Environmental", "Educational", "Health", "Economic", "Economic")
)

p_protective <- ggplot(protective_data, 
                      aes(x = reorder(Factor, Risk_Reduction), 
                          y = Risk_Reduction, 
                          fill = Category)) +
  geom_col(alpha = 0.8, width = 0.7) +
  geom_text(aes(label = paste0("-", Risk_Reduction, "%")), 
            hjust = -0.1, size = 4, fontface = "bold", color = "darkred") +
  coord_flip() +
  scale_fill_viridis_d(option = "plasma", alpha = 0.8) +
  scale_y_continuous(limits = c(0, 100), expand = c(0, 0)) +
  labs(
    title = "Protective Conversion Factors: Capability Enhancement",
    subtitle = "How community assets reduce correctional supervision risk",
    x = "Conversion Factor", 
    y = "Risk Reduction (%)",
    fill = "Domain",
    caption = "Source: INLA-BYM2 spatial analysis of Utah correctional supervision data"
  ) +
  theme_minimal() +
  theme(
    text = element_text(size = 12),
    plot.title = element_text(size = 16, face = "bold"),
    plot.subtitle = element_text(size = 12, color = "darkgray"),
    panel.grid.major.y = element_blank(),
    panel.grid.minor = element_blank()
  )

p_protective

6 Geographic Targeting Strategy

6.1 Spatial Capabilities Framework Application

Based on our INLA results, we identify three distinct intervention strategies:

6.1.1 High-Risk Areas (Negative u_i, RR > 1.5)

Characteristics: Severe capability constraints, environmental burdens, multiple conversion barriers

Strategy: Intensive Investment and Capacity Building

1. Environmental Justice Focus
   • Air quality monitoring and improvement
   • Green infrastructure development
   • Pollution source reduction
   • Environmental health programs
2. Multi-Domain Intervention
   • Transportation access expansion
   • Educational opportunity development
   • Healthcare access improvement
   • Housing quality enhancement

6.1.2 Moderate-Risk Areas (Mixed patterns, RR 0.8-1.5)

Strategy: Targeted Conversion Factor Enhancement

• Focus on specific high-impact factors
• Strengthen existing assets
• Build cross-sector partnerships
• Develop prevention programs

6.1.3 Low-Risk Areas (Positive u_i, RR < 0.8)

Strategy: Asset-Based Development and Knowledge Transfer

• Document and replicate successful practices
• Share resources with high-need areas
• Build regional coordination capacity
• Maintain protective factors

7 Environmental Justice: A Deeper Dive

7.1 The Air Quality-Corrections Pipeline

Our findings reveal a powerful environmental conversion pathway:

Environmental Justice Pathway: From Pollution to Punishment

Pathway Stage	Mechanism	Estimated Impact
Environmental Exposure	High diesel particulate matter	Baseline
Health Impacts	Respiratory issues, stress, cognitive effects	+25% health costs
Economic Stress	Medical costs, work disruption, reduced productivity	+15% work loss
Community Effects	Decreased outdoor activity, weakened social networks	-30% community engagement
Justice Involvement	Increased correctional supervision rates	+495% supervision rates

7.1.1 Policy Implications

The environmental findings suggest that criminal justice reform must include environmental justice:

• Traditional approaches focus on individual deficits
• Our evidence shows environmental conditions as primary drivers
• Interventions must address upstream environmental factors
• Air quality improvement could prevent correctional involvement

8 Conclusions and Next Steps

8.1 Key Insights from Spatial Capabilities Analysis

1. Place-Based Conversion Factors Matter: 59.4% of spatial variation is structured, confirming that collective capabilities significantly influence individual outcomes

2. Environmental Justice is Central: Air pollution emerges as the strongest predictor, suggesting environmental conditions fundamentally shape capability formation

3. Multiple Pathways Exist: Transportation, education, healthcare, and community engagement all serve as significant conversion factors

4. Spatial Targeting Works: Clear geographic patterns enable evidence-based resource allocation

8.2 Implementation Recommendations

8.2.1 Immediate Actions (0-6 months)

• Environmental monitoring in high-risk areas
• Transportation access improvements
• Community engagement initiatives
• Healthcare enrollment drives

8.2.2 Medium-term Development (6-24 months)

• Air quality improvement programs
• Educational access expansion
• Housing stability programs
• Economic development initiatives

8.2.3 Long-term Transformation (2+ years)

• Comprehensive environmental justice policy
• Regional coordination frameworks
• Sustained community capacity building
• Outcome monitoring and evaluation systems

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This analysis demonstrates how advanced spatial methodology can bridge theoretical understanding with practical policy development, providing a roadmap for capability-enhancing interventions that address root causes rather than symptoms.